A head for a mop is disclosed in ES 1047176 U. For the assembly of a mop head, several cleaning strips are placed one over the other, twisted with respect to each other and then affixed to the mop head. The cleaning strips are distributed over the circumference on the finished mop head and they hang from the mop head in the shape of a bell. The cleaning strips can be made of various textile materials. For example, the use of microfibers or nonwovens fixed by a binder as a textile material is known. The textile materials are suitable for absorbing water and also grease and for binding particles. Furthermore, the affixing of an abrasive body to the mop head is known. It can be found between the mop head and the cleaning strips or below the cleaning strips. If the abrasive body is below the cleaning strips, it can be difficult to bring it into contact with the floor to be cleaned since it is mostly covered by cleaning strips. If the abrasive body is located between the mop head and the cleaning strips, it sticks out mostly radially from the mop head and in this way it also can be difficult to bring into contact with the floor to be cleaned and only provides a small contact area.